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The model of a topological quantum computer is a promising one due to its natural resistance to noise and other errors. Operations in such a computer are implemented by braiding the trajectories of anyons. While it is easy to understand how…

Unitary braiding operators can be used as robust entangling quantum gates. We introduce a solution-generating technique to solve the $(d,m,l)$-generalized Yang-Baxter equation, for $m/2\leq l \leq m$, which allows to systematically…

Topological quantum computation by way of braiding of Majorana fermions is not universal quantum computation. There are several attempts to make universal quantum computation by introducing some additional quantum gates or quantum states.…

We propose a dual-architecture quantum simulation framework for modeling morphisms and stability conditions in the bounded derived category $\mathbf{D}^b(\mathrm{Coh}(X))$, with applications to D-brane physics on K\"ahler and non-K\"ahler…

Harnessing non-abelian statistics of anyons to perform quantum computational tasks is getting closer to reality. While the existence of universal anyons by braiding alone such as the Fibonacci anyon is theoretically a possibility,…

Non-semisimple extensions of the Ising anyon model developed in our previous work enable universal topological quantum computation via braiding alone, overcoming the Clifford-only limitation of semisimple theories. The non-semisimple theory…

We investigate a promising conformal field theory realization scheme for topological quantum computation based on the Fibonacci anyons, which are believed to be realized as quasiparticle excitations in the $\mathbb{Z}_3$ parafermion…

The Yang-Baxter equation and it's various forms have applications in many fields, including statistical mechanics, knot theory, and quantum information. Unitary solutions of the braided Yang-Baxter equation are of particular interest as…

Braiding defects in topological stabiliser codes has been widely studied as a promising approach to fault-tolerant quantum computing. Here, we explore the potential and limitations of such schemes in codes of all spatial dimensions. We…

We study an efficient algorithm to hash any single qubit gate (or unitary matrix) into a braid of Fibonacci anyons represented by a product of icosahedral group elements. By representing the group elements by braid segments of different…

Quantum compiling, which aims to approximate target qubit gates by finding optimal sequences (braidwords) of basic braid operations, constitutes a fundamental challenge in quantum computing. We develop a genetic algorithm (GA)-enhanced…

In a topological quantum computer, universality is achieved by braiding and quantum information is natively protected from small local errors. We address the problem of compiling single-qubit quantum operations into braid representations…

We show that universal quantum computation can be performed within the ground state of a topologically ordered quantum system, which is a naturally protected quantum memory. In particular, we show how this can be achieved using brane-net…

In topologically-protected quantum computation, quantum gates can be carried out by adiabatically braiding two-dimensional quasiparticles, reminiscent of entangled world lines. Bonesteel et al. [Phys. Rev. Lett. 95, 140503 (2005)], as well…

In a topological quantum computer, braids of non-Abelian anyons in a (2+1)-dimensional space-time form quantum gates, whose fault tolerance relies on the topological, rather than geometric, properties of the braids. Here we propose to…

We propose an effective set of elementary quantum gates which provide an encoded universality and demonstrate the physical feasibility of these gates for the solid-state quantum computer based on the multi-atomic systems in the QED cavity.…

Non-Abelian topological order (TO) enables topologically protected quantum computation with its anyonic quasiparticles. Recently, TO with $S_3$ gauge symmetry was identified as a sweet spot -- simple enough to emerge from finite-depth…

Majorana-based quantum gates are not complete for performing universal topological quantum computation while Fibonacci-based gates are difficult to be realized electronically and hardly coincide with the conventional quantum circuit models.…

Read-Rezayi fractional quantum Hall states are among the prime candidates for realizing non-Abelian anyons which in principle can be used for topological quantum computation. We present a prescription for efficiently finding braids which…

Universal quantum computation (UQC) using Majorana fermions on a 2D topological superconducting (TS) medium remains an outstanding open problem. This is because the quantum gate set that can be generated by braiding of the Majorana fermions…